Christmas tree lights - surprisingly cool

Let me start off by saying I think I first read about this on HowStuffWorks.com (many years ago). So, why are christmas lights so cool? They are cool because they are a whole bunch of lights in series, but they still work if one of the bulbs gets burnt out. If you are not familiar with circuits, a series circuit is one in which all of the current goes through all of the items in that circuit (as compared to the case where the current gets split up). Here is an example of a series circuit with two bulbs.

In this case, the current comes out of the battery, goes through one filament and then the other. Both bulbs light. What happens if one of the filaments break? Then there would be no complete path for the current and thus no current. No light in either bulb.

If you remove one bulb in a string of christmas lights, they all go out. This indicates they are in series. However, if you break one of the bulbs and leave it in, the other lights stay on.

So how does this work?

Let me start with some more fundamental ideas. There is really a lot going on here, but I will kind of jump in the middle of it.

Key Idea 1: Voltage Loop rule

Also, this is called Kirchhoff's loop rule (just in case you go by that name). This says that the change in potential around a closed loop is zero volts. Or, you could say that if you add up all the changes in potential around any loop of a circuit, they must add to zero. Note that there are some cases where this is not true (in particular cases with changing magnetic field - but that I won't go there). Electric potential is really just the change in electric potential ENERGY per charge - so this whole thing comes from the work-energy equation.

Key Idea 2: Ohm's Law

This says that the change in potential across some element in a circuit is proportional to the current going through that element (like a resistor or a lightbulb). The proportionality constant is the resistance. This is called Ohm's Law.

I am mostly ready to talk about the lights now - but I will say that I should come back to this and explain in more fundamental terms. So, what happens when the lights are working normally? They are connected to an oscillating 120 volts powersource, but let's pretend it is a DC source for now. If I use the loop rule, then potential across all 50 lights will be 120 volts (they are like resistors). They all have the same resistance and the same current, so each one has 2.4 volts across it. Everybody is happy. But now, suppose one of the filaments in one of the bulbs breaks. Now there will be no current. However, the loop rule has to still work. This means that if there is 0 volts across all the unbroken lights (no current), then the 1 broken light will have to have 120 volts across it. Here is an example with just two bulbs:

Now with 120 volts across one of these broken christmas bulbs, something happens. Here is a close up view of a broken bulb.

This "extra wire" has some type of insulating coating on it so that it normally does nothing. When 120 volts is applied across the insulator something happens and makes it a conductor. I am not exactly sure what happens, but I guess it is something like a spark through the material that makes it either melt or become a conductor. Either way, after applying the 120 volts, the extra wire allows the current to once again flow through all the other lights.